Project-Based Learning with ODEs: Modeling Straw Rocket Motion with Air Resistance

Authors

Viktoria Savatorova, Central Connecticut State UniversityFollow
Ethan Dyer, Central Connecticut State University
Aleksei Talonov, University of Nevada Las Vegas

Publication Date

8-20-2025

Keywords

Mathematical modeling, projectile motion, quadratic drag, data fitting, parameter estimation

Disciplines

Applied Mathematics | Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

This paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and drag coefficient. These parameters are then used to predict the outcomes of angled launches, highlighting asymmetries in flight time and range caused by drag. The activity connects theoretical modeling with experimentation and provides students with hands-on experience in testing assumptions, fitting parameters, and validating models.

Recommended Citation

Savatorova, Viktoria; Dyer, Ethan; and Talonov, Aleksei (2025) "Project-Based Learning with ODEs: Modeling Straw Rocket Motion with Air Resistance," CODEE Journal: Vol. 19, Article 2.
Available at: https://scholarship.claremont.edu/codee/vol19/iss1/2